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Shigeru Furuichi

Publications and source records attributed to Shigeru Furuichi.

At least 73 records · Page 4Linked to original sources
arXiv2012

Schrödinger uncertainty relation, Wigner-Yanase-Dyson skew information and metric adjusted correlation measure

In this paper, we give a Schrödinger-type uncertainty relation using the Wigner-Yanase-Dyson skew information. In addition, we give Schrödinger-type uncertainty relation by use of a two-parameter extended correlation measure. Moreover, we give the further generalization for Schrödinger-type uncertainty relation by metric adjusted correlation measure. These results generalize our previous result in [Phys. Rev. A, Vol.82(2010), 034101].

quant-ph↗
arXiv2011

On refined Young inequalities and reverse inequalities

In this paper, we show refined Young inequalities for two positive operators. Our results refine the ordering relations among the arithmetic mean, the geometric mean and the harmonic mean for two positive operators. In addition, we give two different reverse inequalities for the refined Young inequality for two positive operators.

math.FA↗
arXiv2011

Several applications of Cartwright-Field's inequality

In this paper we present several applications of Cartwright-Field's inequality. Among these we found Young's inequality, Bernoulli's inequality, the inequality between the weighted power means, Hölder's inequality and Cauchy's inequality. We give also two applications related to arithmetic functions and to operator inequalities.

math.CA↗
arXiv2011

Refined Young inequalities with Specht's ratio

In this paper, we show that the $ν$-weighted arithmetic mean is greater than the product of the $ν$-weighted geometric mean and Specht's ratio. As a corollary, we also show that the $ν$-weighted geometric mean is greater than the product of the $ν$-weighted harmonic mean and Specht's ratio. These results give the improvements for the classical Young inequalities, since Specht's ratio is generally greater than 1. In addition, we give an operator inequality for positive operators, applying our refined Young inequality.

math.FA↗
arXiv2010

A generalized Faddeev's axiom and the uniqueness theorem for Tsallis entropy

The uniequness theorem for the Tsallis entropy by introducing the generalized Faddeev's axiom is proven. Our result improves the recent result, the uniqueness theorem for Tsallis entropy by the generalized Shannon-Khinchin's axiom in \cite{Suy}, in the sence that our axiom is simpler than his one, as similar that Faddeev's axiom is simpler than Shannon-Khinchin's one.

cond-mat.stat-mech↗
arXiv2010

An axiomatic characterization of a two-parameter extended relative entropy

The uniqueness theorem for a two-parameter extended relative entropy is proven. This result extends our previous one, the uniqueness theorem for a one-parameter extended relative entropy, to a two-parameter case. In addition, the properties of a two-parameter extended relative entropy are studied.

cond-mat.stat-mech↗
arXiv2010

On bounds of Tsallis relative entropy and an inequality for generalized skew information

Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory in quantum information science. In this paper, we study some properties for information quantities in quantum system through trace inequalities. Especially, we give upper bounds and lower bounds of Tsallis relative entropy, which is a one-parameter extension of the relative entropy in quantum system. In addition, we compare the known bounds and the new bounds, for both upper and lower bounds, respectively. We also give an inequality for generalized skew information by introducing a generalized correlation measure.

math.FA↗
arXiv2010

A matrix trace inequality and its application

In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson inequality for positive semidefinite matrices.

math.FA↗
arXiv2010

Characterizations of generalized entropy functions by functional equations

We shall show that a two-parameter extended entropy function is characterized by a functional equation. As a corollary of this result, we obtain that the Tsallis entropy function is characterized by a functional equation, which is a different form used in \cite{ST} i.e., in Proposition \ref{prop01} in the present paper. We also give an interpretation of the functional equation giving the Tsallis entropy function, in the relation with two non-additive properties.

cs.IT↗
arXiv2010

Matrix trace inequalities on the Tsallis entropies

Maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for non-negative matrices in the framework of matrix analysis. In addtition, some matrix trace inequalities related to the Tsallis relative entropy are studied.

cond-mat.stat-mech↗
arXiv2010

A generalized Fannes inequality

We axiomatically characterize the Tsallis entropy of a finite quantum system. In addition, we derive a continuity property of Tsallis entropy. This gives a generalization of the Fannes inequality.

quant-ph↗
arXiv2010

On a parametrically extended entanglement-measure due to Tsallis relative entropy

In the previous paper \cite{FYK}, we mainly studied the mathematical properties of Tsallis relative entropy with respect to the density operators. As an application of it, we adopt a parametrically extended entanglement-measure due to Tsallis relative entropy in order to measure the degree of entanglement. Then we study its properies with respect to the parameter $q$ appearing in Tsallis entropies. In addition, the relation between it and the relative entropy of entanglement is studied.

quant-ph↗
arXiv2010

On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics

We give a new proof of the theorems on the maximum entropy principle in Tsallis statistics. That is, we show that the $q$-canonical distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the $q$-expectation value and the $q$-Gaussian distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the $q$-variance, as applications of the nonnegativity of the Tsallis relative entropy, without using the Lagrange multipliers method. In addition, we define a $q$-Fisher information and then prove a $q$-Cramér-Rao inequality that the $q$-Gaussian distribution with special $q$-variances attains the minimum value of the $q$-Fisher information.

cond-mat.stat-mech↗
arXiv2006

Trace inequalities in nonextensive statistical mechanics

In this short paper, we establish a variational expression of the Tsallis relative entropy. In addition, we derive a generalized thermodynamic inequality and a generalized Peierls-Bogoliubov inequality. Finally we give a generalized Golden-Thompson inequality.

cond-mat.stat-mech↗